Materials for engineering, 3rd Edition - (Malestrom)

Composite materials 207
τ
r
P
P – dP
dx
6.17 Element of fibre in Fig. 6.16.
As shown in Fig. 6.18(a), the stress in the fibre increases linearly from each
end, reaching a maximum at the centre of the fibre, where x = l/2.
With increasing length of fibre, the maximum stress carried by the fibre
increases until it reaches σ f
*
when fibre failure will occur. The distance from
one fibre end to the point of maximum stress is known as the ‘transfer
length’ (l/2) and, for the whole fibre, the critical transfer length (l c ) is required
to achieve a stress of σ f * . Figure 6.18 shows the variation of tensile stress in
a fibre as a function of fibre length: if the fibre is shorter than l c , σ cannot
reach the value for fibre fracture however much the composite is deformed.
The critical aspect ratio for a fibre to be broken is thus:
l
d
c f *
σ
= 2 τ
max
and only by using fibres much longer than l c can the full strengthening
potential of the reinforcement be achieved.
Stress in fibre (σ)
σ f
*
σ f
*
I
(a)
6.18 Stress along fibre (a) l < l c and (b) l = l c .
I
(b)